Pot Pie

Name: Pot Pie
Ingredients: 4 Tablespoons Butter; 1/2 cup Finely Diced Onion; 1/2 cup Finely Diced Carrot; 1/2 cup Finely Diced Celery; 3 cups Shredded Cooked Chicken Or Turkey; 1/4 cup Flour; 3 cups Low-sodium Chicken Broth, Plus More If Needed; Splash Of White Wine (optional); 1/4 teaspoon Turmeric; Salt And Pepper, to taste; Chopped Fresh Thyme To Taste; 1/4 cup Half-and-half Or Cream; 1 whole Unbaked Pie Crust; 1 whole Egg; 2 Tablespoons Water